[BOOK][B] Brownian motion
This eagerly awaited textbook covers everything the graduate student in probability wants to
know about Brownian motion, as well as the latest research in the area. Starting with the …
know about Brownian motion, as well as the latest research in the area. Starting with the …
[BOOK][B] Random walk: a modern introduction
GF Lawler, V Limic - 2010 - books.google.com
Random walks are stochastic processes formed by successive summation of independent,
identically distributed random variables and are one of the most studied topics in probability …
identically distributed random variables and are one of the most studied topics in probability …
Scaling limits of loop-erased random walks and uniform spanning trees
O Schramm - Israel Journal of Mathematics, 2000 - Springer
The uniform spanning tree (UST) and the loop-erased random walk (LERW) are strongly
related probabilistic processes. We consider the limits of these models on a fine grid in the …
related probabilistic processes. We consider the limits of these models on a fine grid in the …
[PDF][PDF] Recombination: A family of Markov chains for redistricting
Redistricting is the problem of partitioning a set of geographic units into a fixed number of
subsets called districts, subject to a list of rules and priorities. These districts are used for …
subsets called districts, subject to a list of rules and priorities. These districts are used for …
Conformal invariance of planar loop-erased random walks and uniform spanning trees
GF Lawler, O Schramm, W Werner - Selected Works of Oded Schramm, 2011 - Springer
This paper proves that the scaling limit of a loop-erased random walk in a simply connected
domain D\mathop ⊂\limits_ ≠ C is equal to the radial SLE 2 path. In particular, the limit …
domain D\mathop ⊂\limits_ ≠ C is equal to the radial SLE 2 path. In particular, the limit …
Conformally invariant scaling limits: an overview and a collection of problems
O Schramm - Selected Works of Oded Schramm, 2011 - Springer
Many mathematical models of statistical physics in two dimensions are either known or
conjectured to exhibit conformal invariance. Over the years, physicists proposed predictions …
conjectured to exhibit conformal invariance. Over the years, physicists proposed predictions …
Nodal portraits of quantum billiards: Domains, lines, and statistics
This is a comprehensive review of the nodal domains and lines of quantum billiards,
emphasizing a quantitative comparison of theoretical findings to experiments. The nodal …
emphasizing a quantitative comparison of theoretical findings to experiments. The nodal …
Theoretical studies of self-organized criticality
D Dhar - Physica A: Statistical Mechanics and its Applications, 2006 - Elsevier
These notes are intended to provide a pedagogical introduction to the abelian sandpile
model of self-organized criticality, and its related models. The abelian group, the algebra of …
model of self-organized criticality, and its related models. The abelian group, the algebra of …
Values of Brownian intersection exponents, I: Half-plane exponents
GF Lawler, O Schramm, W Werner - Selected Works of Oded Schramm, 2011 - Springer
Theoretical physics predicts that conformal invariance plays a crucial role in the
macroscopic behavior of a wide class of two-dimensional models in statistical physics (see …
macroscopic behavior of a wide class of two-dimensional models in statistical physics (see …
The dimension of the SLE curves
V Beffara - 2008 - projecteuclid.org
The dimension of the SLE curves Page 1 The Annals of Probability 2008, Vol. 36, No. 4,
1421–1452 DOI: 10.1214/07-AOP364 © Institute of Mathematical Statistics, 2008 THE …
1421–1452 DOI: 10.1214/07-AOP364 © Institute of Mathematical Statistics, 2008 THE …